曲率差分驱动的极小曲面滤波器

王满利; 田子建; 张元刚

doi:10.11999/JEIT190216

引用本文: 王满利, 田子建, 张元刚. 曲率差分驱动的极小曲面滤波器[J]. 电子与信息学报, 2020, 42(3): 764-771. doi: 10.11999/JEIT190216 shu

Citation: Manli WANG, Zijian TIAN, Yuangang ZHANG. Minimal Surface Filter Driven by Curvature Difference[J]. Journal of Electronics and Information Technology, 2020, 42(3): 764-771. doi: 10.11999/JEIT190216 shu

曲率差分驱动的极小曲面滤波器

1.
中国矿业大学（北京）机电与信息工程学院北京 100083
2.
河南理工大学物理与电子信息学院焦作 454000
3.
兖矿集团信息化管理中心邹城 273500

作者简介: 王满利: 男，1981年生，博士生，研究方向为信息与通信工程;
田子建: 男，1964年生，教授，研究方向为信息与通信工程;

通讯作者: 田子建,tianzj0726@126.com

基金项目: 国家自然科学基金（51674269）

摘要: 为提高全变分图像降噪模型的降噪性能和边缘保持性能，该文提出一种曲率差分驱动的极小曲面滤波器。首先，在平均曲率滤波器模型基础上，引入自适应曲率差分边缘探测函数，建立曲率差分驱动的极小曲面滤波器模型；接着，从微分几何理论角度，阐述该能量泛函模型的物理意义和平均曲率能量减小方法；最后，在离散的图像域，通过迭代的方式使图像每个像素邻域内的曲面向极小曲面迭代进化，实现能量泛函的平均曲率能量极小化，从而能量泛函的总能量也完成极小化。实验表明，该滤波器不仅能去除高斯噪声、椒盐噪声，还能去除这两类噪声构成的混合噪声，其降噪性能和边缘保持性能优于同类型的其他5种全变分算法。

关键词:

English

Minimal Surface Filter Driven by Curvature Difference

1.
School of Mechanical Electronic & Information Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China
2.
School of Physics &Electronic Information Engineering, HeNan Polytechnic University, Jiaozuo 454000, China
3.
Information Center of YanKuang Group, Zoucheng 273500, China

Corresponding author: Zijian TIAN,tianzj0726@126.com

Received Date: 2019-04-04
Accepted Date: 2019-10-26
Available Online: 2020-03-01
Fund Project: The National Natural Science Foundation of China (51674269)

Abstract: To improve performance of denoising and edge preservation of the total variational image denoising model, a curvature difference driven minimal surface filter is proposed. Firstly, the presented filter model is constructed by adding an adaptive edge detection function of curvature difference to the mean curvature filter model. After that, from the perspective of differential geometry theory, the physical meaning of the energy functional model and the method of reducing the average curvature energy are elaborated. Finally, in the discrete image domain, the surface in the neighborhood of each pixel of the image is iteratively evolved to the minimal surface to minimize the average curvature energy of the energy functional, so that the total energy of the energy functional is also minimized. Experiments show that the filter can not only remove Gauss noise and salt and pepper noise, but also remove the mixed noise composed of these two kinds of noise. Its performance of noise reduction and edge preservation is better than the other five total variational algorithms of the same kind.

Key words:

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图 1 图像域Ω分解方法

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图 2 u_i‚j邻域内3点的组合关系

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图 3 d_k的近似求解方法

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图 4 MSF滤波器能量变化曲线

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图 5 MCF和MSF的降噪比较

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图 6 相同迭代次数下两滤波器降噪结果对比

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图 7 6种算法的降噪图像评价指标和运行时间比较

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图 8 MSF去除混合噪声的降噪图像对比

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表 1 降噪图像的评价指标数据

噪声类型	图像	滤波器	噪声方差噪声密度	迭代次数	PSNR.N	PSNR.D	CDE	RFSIM
高斯噪声	Lena	MSF	10	10	28.1111	32.5290	12.3499	0.6873
		MSF	20	20	22.1472	28.8819	12.3575	0.5065
		MCF	10	10	28.1111	31.2486	12.3128	0.6063
		MCF	20	20	22.1472	28.7087	12.3020	0.4644
	House	MSF	5	7	34.1560	35.9549	11.0543	0.6838
			10	10	28.1072	32.4532	11.0582	0.5043
			20	20	22.1129	28.5565	11.0600	0.3117
		MCF	5	7	34.1560	33.1901	11.0436	0.5879
			10	10	28.1072	31.1816	11.0491	0.4750
			20	20	22.1129	28.3753	11.0487	0.3315
椒盐噪声	peppers	MSF	0.05	4	18.2659	34.3401	12.3245	0.8842
		MSF	0.10	9	15.3176	32.0921	12.3229	0.8271
		MCF	0.05	4	18.2659	30.1227	12.3089	0.7940
		MCF	0.10	9	15.3176	30.5087	12.2877	0.7083